The specific heat of fat is 0.45 cal/(g ⋅ °C) (1.9 J/g °C) and the density of fat is 0.94 g/cm3. How much energy (in calories and joules) is needed to heat 10 cm3 of fat from room temperature (25 °C) to its melting point (35 °C)?

Ch.1 Matter and Measurements

McMurry - Fundamentals of General, Organic, and Biological Chemistry 8th Edition

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McMurry 8th Edition

Ch.1 Matter and Measurements

문제 83

1장, 문제 83

The specific heat of fat is 0.45 cal/(g ⋅ °C) (1.9 J/g °C) and the density of fat is 0.94 g/cm³. How much energy (in calories and joules) is needed to heat 10 cm³ of fat from room temperature (25 °C) to its melting point (35 °C)?

검증된 단계별 안내

Step 1: Identify the formula for calculating the energy required to heat a substance. The formula is: Q = m × c × ΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Step 2: Calculate the mass of the fat using its density and volume. The formula for mass is: m = density × volume. Given the density of fat is 0.94 g/cm³ and the volume is 10 cm³, substitute these values into the formula.

Step 3: Determine the temperature change (ΔT). Subtract the initial temperature (25 °C) from the final temperature (35 °C): ΔT = 35 °C - 25 °C.

Step 4: Substitute the values for mass (from Step 2), specific heat capacity (c = 0.45 cal/(g⋅°C) or 1.9 J/(g⋅°C)), and ΔT (from Step 3) into the formula Q = m × c × ΔT. Perform the calculation separately for calories and joules.

Step 5: Report the energy required in both calories and joules. Ensure the units are consistent and clearly labeled for each result.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Specific Heat Capacity

Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. In this case, the specific heat of fat is given as 0.45 cal/(g ⋅ °C) or 1.9 J/g °C, indicating how much energy is needed to increase the temperature of fat. Understanding this concept is crucial for calculating the energy required to heat the fat.

Density

Density is defined as mass per unit volume and is a key property of materials. The density of fat is provided as 0.94 g/cm³, which allows us to determine the mass of the fat when its volume is known. This relationship is essential for converting volume measurements into mass, which is necessary for energy calculations involving specific heat.

Energy Calculation

Energy calculation in this context involves using the formula Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. To find the energy needed to heat the fat from 25°C to 35°C, we must first calculate the mass of the fat using its density and volume, then apply the specific heat capacity to find the total energy required in both calories and joules.